Question

∆ABC with Prove: Statement Reason 1. given 2. ∠CAB ≅ ∠EDB ∠ACB ≅ ∠DEB If two parallel lines are cut by a transversal, the corresponding angles are congruent. 3. ∆ABC ~ ∆DBE AA criterion for similarity 4. Corresponding sides of similar triangles are proportional. 5. AB = AD + DB CB = CE + EB segment addition 6. Substitution Property of Equality 7. division 8. Subtraction Property of Equality What is the missing statement in the proof? Scroll down to see the entire proof. A. B. C. D.

Answer 1

Answer with Step-by-step explanation:

We are given that a triangle ABC

$DE\parallel AC$

We prove that $\frac{AD}{DB}=\frac{CE}{EB}$

We have to find the missing step in given proof.

Proof:

1.Statement:$DE\parallel AC$

Reason: Given

2.Statement:$\angle CAB\cong \angle EDB. \angle ACB\cong\angle DEB$

Reason:If two parallel lines are cut by a transversal line then, congruent angles are congruent.

3.Statement:$\triangle ABC\cong \triangle DBE$

Reason: AA criterion for similarity

4.Statement:$\frac{AB}{DB}=\frac{CB}{EB}$

Reason:Corresponding sides of similar triangles are proportional

5.$AB=AD+DB, CB=CE+EB$

Reason: Segment addition property

6.Statement:$\frac{AD+DB}{DB}=\frac{CE+EB}{EB}$

Reason:Substitution property of equality

7.Statement:$\frac{AD}{DB}+1=\frac{CE}{EB}+1$

Reason:Division property

8.Statement:$\frac{AD}{DB}=\frac{CE}{EB}$

Reason: Subtraction property of equality

Hence, proved.